Polymer engineering involves making mutations (atomic replacement, insertion, or deletion) in a polymer of known sequence and structure, and evaluating the effects of such mutations on the physical and biological properties of the polymer. A central approach to an understanding of the effects of a mutation is to estimate the difference in conformational flexibility between the native polymer and the derivation of the polymer (where the derivation of the polymer has the mutation) in the region near the site of the mutation.
To assist in this approach, many measures of conformational flexibility can be defined, including the root-mean square fluctuation, and the Boltzmann entropy. From a thermodynamic standpoint, the entropy provides the most natural means of quantifying the flexibility in a polymer. However, when two polymers of different primary sequence are compared, differences in the total molecular entropy may not be informative due to the different number of degrees of freedom in the two polymers. For example, consider a mutation in a protein that changes a large residue to one that is significantly smaller. The total molecular entropy of the mutated (derived) protein may be lower than the total molecular entropy of the native protein, despite an increase in the conformational freedom of the derived protein about the mutation site, simply because a small residue intrinsically has less conformational flexibility than a large residue. From an engineering standpoint however, the obvious reduction in entropy resulting from the shift from a large to a small residue is not of primary interest, while the small increase in the conformational freedom of the environment about the residue is very important.
As the above illustrates, when computing the effects of a mutation on the conformational flexibility of a polymer, there is a clear need to compensate for the size difference between mutant and wild type residues, or to separate the contributions of the mutated residue and the environment about the residue to the total entropy. Given the above background, there is a need for improved tools for studying and quantifying the thermodynamic effects of mutations in polymers.